🧮 algebra

1. **State the problem:** We want to find the long-term amount of warfarin in the body, given that each day a 5 mg dose is taken and 8% of the drug remains after 24 hours. 2. **Def

1. The problem is to analyze and graph the quadratic function $f(x) = 3x^2 + 3x - 6$. 2. The general form of a quadratic function is $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$

1. **State the problem:** We are given a point $P(-2, -3)$ and need to find a second point that is 4 units away from $P$ and has an $x$-coordinate of $-2$. 2. **Formula used:** The

1. **State the problem:** Kent mixed oil and gas in a ratio of 8 fluid ounces of oil for every 1 gallon of gas. We need to determine which of the given statements are true based on

1. The problem is to evaluate the expression $25^{\frac{1}{2}}$. 2. Recall that raising a number to the power of $\frac{1}{2}$ is equivalent to taking the square root of that numbe

1. **Problemstellung:** Vereinfache die gegebenen Terme mithilfe der Potenzgesetze so weit wie möglich und schreibe sie, wenn möglich, als Wurzel. 2. **Wichtige Potenzgesetze:**

1. Il problema chiede di calcolare quanti giorni servono per finire One Piece, sapendo che la durata totale è di 24.000 minuti e che ogni giorno si guardano solo le ore diurne, cio

1. **State the problem:** Simplify the expression $(2x) + (-2x)$. 2. **Recall the rule:** Adding a number and its opposite (negative) results in zero. In algebra, $a + (-a) = 0$.

1. **State the problem:** Find the area of triangle $\triangle ABC$ where lines $l_1: y = -2x + 6$ and $l_2: y = x + 3$ intersect at point $A$. Line $l_1$ meets the x-axis at $C$,

1. **State the problem:** Find the area of quadrilateral O C B E formed by the intersection of lines $l_1: y=3x+5$ and $l_2: y=-2x+6$ and the coordinate axes. 2. **Find points of i

1. State the problem: Evaluate the expression $x \cdot y$ for $x=3$ and $y=9$. 2. Write the original expression:

1. **State the problem:** Determine whether each given mapping diagram represents a function. 2. **Recall the definition of a function:** A function is a relation where each input

1. Problemet: Lös ekvationen $$3x + 5 = 20$$ för $x$. 2. Formeln och regler: För att lösa en linjär ekvation isolerar vi variabeln $x$ genom att använda inversa operationer, såsom

1. **State the problem:** Simplify the expression $\left(\frac{1}{5^2}\right)^3$. 2. **Recall the exponent rule:** When raising a power to another power, multiply the exponents: $\

1. **Problem:** Simplify the expression $\frac{2a-8}{2}$ and state any excluded values. 2. **Formula and rules:** To simplify a rational expression, factor numerator and denominato

1. **State the problem:** Solve the quadratic equation $3x^2 + 18 = 5x$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. Let's start by understanding what a fraction is. A fraction represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator (top number) and $b$ is the d

1. **State the problem:** Prove that the quadratic equation $ax^2 + bx + c = 0$, where $a, b, c$ are real numbers and $a > 0$, has two real distinct solutions if and only if $b^2 >

1. **State the problem:** We are given several exponential functions and need to find for each:

1. **State the problem:** Determine which tables represent exponential functions and analyze given exponential functions for asymptotes, y-intercepts, domain, and range. 2. **Check

1. **State the problem:** Find the equation of the line passing through the point $(-5, 12)$ and perpendicular to the line given by $$y = \frac{2}{3}x + 14.$$ 2. **Recall the formu